A constant equation of state \(w=p/\rho =P/\mu \)  has observational preferred value around \(w=-1\) , i.e. near the value of a cosmological constant (see for instance [1]}). Wormholes with similar equation of state have been studied in [2]}, [3]}, with \(p\ne -\tau \)  in [4]}, [5]}, [6]} or with \(\tau =w\rho \)  in [7]}. From the pressure (REF ), we derive that a constant equation of state \(w\)  is obtained when
\(\mu =\left[-1+\operatorname{arctanh}\beta (1+2\operatorname{arctanh}\theta )\right]/w\) 
